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          数组排序
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        <p><a target="_blank" rel="noopener" href="https://leetcode-cn.com/problems/sort-an-array/">LeetCode原题</a><br>难度 <code>中等</code></p>
<p>给你一个整数数组 nums，将该数组升序排列。</p>
<p>示例 1：</p>
<blockquote>
<p>输入：nums = [5,2,3,1]<br>输出：[1,2,3,5]</p>
</blockquote>
<p>示例 2：</p>
<blockquote>
<p>输入：nums = [5,1,1,2,0,0]<br>输出：[0,0,1,1,2,5]</p>
</blockquote>
<p>提示：</p>
<blockquote>
<p>1 &lt;= nums.length &lt;= 50000<br>-50000 &lt;= nums[i] &lt;= 50000</p>
</blockquote>
<a id="more"></a>

<p>这道题在LeetCode中难度是中等，可能看上去很简单，因为我们随手可以写出的排序算法就有很多种，但是如果想要牢靠掌握所有的排序算法还是够得上中等难度的。</p>
<p><img src="https://tva1.sinaimg.cn/large/00831rSTgy1gdd0lpe3c1j314e0jy7ai.jpg" alt="image-20200331124956505"></p>
<p>下面是几种常用算法的整理：</p>
<h2 id="快速排序"><a href="#快速排序" class="headerlink" title="快速排序"></a>快速排序</h2><p>快排是最常用的几种排序方法之一，其主要方法是</p>
<ol>
<li><p>在<code>数组</code>中随机选择一个数作为基准，将该基准放到数组的末端。</p>
</li>
<li><p>将数组中所有数与基准进行对比，将大于基准的数移动至基准的右侧。</p>
</li>
<li><p>将数组左侧和右侧分别试做两个新数组重复步骤1。</p>
</li>
</ol>
<p><img src="https://tva1.sinaimg.cn/large/00831rSTly1gdd3e5ci79g308c050adl.gif" alt="Quicksort-example.gif"></p>
<p><img src="https://tva1.sinaimg.cn/large/00831rSTly1gdd3esbt4xg30mj0707d3.gif" alt="849589-20171015230936371-1413523412.gif"></p>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span>:</span></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">partition</span>(<span class="params">self, nums, l, r</span>):</span></span><br><span class="line">        pivot = nums[l]</span><br><span class="line">        <span class="keyword">while</span> l &lt; r:</span><br><span class="line">            <span class="keyword">while</span> l &lt; r <span class="keyword">and</span> pivot &lt;= nums[r]:</span><br><span class="line">                r -= <span class="number">1</span></span><br><span class="line">            nums[l] = nums[r] </span><br><span class="line">            <span class="keyword">while</span> l &lt; r <span class="keyword">and</span> nums[l] &lt;= pivot:</span><br><span class="line">                l += <span class="number">1</span> </span><br><span class="line">            nums[r] = nums[l]</span><br><span class="line">        nums[l] = pivot</span><br><span class="line">        <span class="keyword">return</span> l</span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">random_partition</span>(<span class="params">self, nums, l, r</span>):</span></span><br><span class="line">        i = random.randint(l, r)</span><br><span class="line">        nums[i], nums[r] = nums[r], nums[i]  </span><br><span class="line">        <span class="keyword">return</span> self.partition(nums, l, r)</span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">quickSort</span>(<span class="params">self, nums, l, r</span>):</span></span><br><span class="line">        <span class="keyword">if</span> l &lt; r:</span><br><span class="line">            k = self.random_partition(nums, l, r)</span><br><span class="line">            self.quickSort(nums, l, k<span class="number">-1</span>)</span><br><span class="line">            self.quickSort(nums, k+<span class="number">1</span>, r)</span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">sortArray</span>(<span class="params">self, nums: List[int]</span>) -&gt; List[int]:</span></span><br><span class="line">        self.quickSort(nums, <span class="number">0</span>, len(nums)<span class="number">-1</span> )</span><br><span class="line">        <span class="keyword">return</span> nums</span><br></pre></td></tr></table></figure>

<h2 id="归并排序"><a href="#归并排序" class="headerlink" title="归并排序"></a>归并排序</h2><p>归并排序的主要思想是递归+重排两个有序数组</p>
<ol>
<li><p>将数组分成两个部分数组，对返回的两个有序数组进行排序</p>
</li>
<li><p>如果部分数组中只有一个元素，直接返回，否则进行步骤1</p>
</li>
<li><p>对两部分分别进行merge，返回排序后的数组</p>
</li>
</ol>
<p><img src="https://tva1.sinaimg.cn/large/00831rSTly1gdd3eznsbtg308c05040s.gif" alt="1252882-20190217215522179-1982419775.gif"></p>
<p><img src="https://tva1.sinaimg.cn/large/00831rSTly1gdd3f58ue5g30mj0e1qcv.gif" alt="849589-20171015230557043-37375010.gif"></p>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span>:</span></span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">sortArray</span>(<span class="params">self, nums: List[int]</span>) -&gt; List[int]:</span></span><br><span class="line">        <span class="keyword">if</span> len(nums) == <span class="number">1</span>: </span><br><span class="line">            <span class="keyword">return</span> nums</span><br><span class="line">        mid = len(nums) // <span class="number">2</span></span><br><span class="line">        <span class="keyword">return</span> merge(self.sortArray(nums[:mid]), self.sortArray(nums[mid:]))</span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">merge</span>(<span class="params">self, left, right</span>):</span></span><br><span class="line">        res = []</span><br><span class="line">        <span class="keyword">while</span> len(left) &gt; <span class="number">0</span> <span class="keyword">and</span> len(right) &gt; <span class="number">0</span>:</span><br><span class="line">            <span class="keyword">if</span> left[<span class="number">0</span>] &lt; right[<span class="number">0</span>]:</span><br><span class="line">                res.append(left.pop(<span class="number">0</span>))</span><br><span class="line">            <span class="keyword">else</span>:</span><br><span class="line">                res.append(right.pop(<span class="number">0</span>))</span><br><span class="line">        res += left</span><br><span class="line">        res += right</span><br><span class="line">        <span class="keyword">return</span> res </span><br></pre></td></tr></table></figure>

<h2 id="堆排序"><a href="#堆排序" class="headerlink" title="堆排序"></a>堆排序</h2><p>堆排序是基于堆这种数据结构所设计的排序算法</p>
<ol>
<li><p>建堆，从底向上调整堆，使得父亲节点比孩子节点值大，构成大顶堆</p>
</li>
<li><p>交换堆顶和最后一个元素，重新调整堆。</p>
</li>
</ol>
<p><img src="https://tva1.sinaimg.cn/large/00831rSTly1gdd3fdaxudg309q07sk90.gif" alt="Heapsort-example.gif"></p>
<p><img src="https://tva1.sinaimg.cn/large/00831rSTly1gdd3fhzlzbg30f70a4u0x.gif" alt="849589-20171015231308699-356134237.gif"></p>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">heap_sort</span>(<span class="params">nums</span>):</span></span><br><span class="line">    <span class="comment"># 调整堆</span></span><br><span class="line">    <span class="comment"># 迭代写法</span></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">adjust_heap</span>(<span class="params">nums, startpos, endpos</span>):</span></span><br><span class="line">        newitem = nums[startpos]</span><br><span class="line">        pos = startpos</span><br><span class="line">        childpos = pos * <span class="number">2</span> + <span class="number">1</span></span><br><span class="line">        <span class="keyword">while</span> childpos &lt; endpos:</span><br><span class="line">            rightpos = childpos + <span class="number">1</span></span><br><span class="line">            <span class="keyword">if</span> rightpos &lt; endpos <span class="keyword">and</span> nums[rightpos] &gt;= nums[childpos]:</span><br><span class="line">                childpos = rightpos</span><br><span class="line">            <span class="keyword">if</span> newitem &lt; nums[childpos]:</span><br><span class="line">                nums[pos] = nums[childpos]</span><br><span class="line">                pos = childpos</span><br><span class="line">                childpos = pos * <span class="number">2</span> + <span class="number">1</span></span><br><span class="line">            <span class="keyword">else</span>:</span><br><span class="line">                <span class="keyword">break</span></span><br><span class="line">        nums[pos] = newitem</span><br><span class="line">    </span><br><span class="line">    <span class="comment"># 递归写法</span></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">adjust_heap</span>(<span class="params">nums, startpos, endpos</span>):</span></span><br><span class="line">        pos = startpos</span><br><span class="line">        chilidpos = pos * <span class="number">2</span> + <span class="number">1</span></span><br><span class="line">        <span class="keyword">if</span> chilidpos &lt; endpos:</span><br><span class="line">            rightpos = chilidpos + <span class="number">1</span></span><br><span class="line">            <span class="keyword">if</span> rightpos &lt; endpos <span class="keyword">and</span> nums[rightpos] &gt; nums[chilidpos]:</span><br><span class="line">                chilidpos = rightpos</span><br><span class="line">            <span class="keyword">if</span> nums[chilidpos] &gt; nums[pos]:</span><br><span class="line">                nums[pos], nums[chilidpos] = nums[chilidpos], nums[pos]</span><br><span class="line">                adjust_heap(nums, pos, endpos)</span><br><span class="line"></span><br><span class="line">    n = len(nums)</span><br><span class="line">    <span class="comment"># 建堆</span></span><br><span class="line">    <span class="keyword">for</span> i <span class="keyword">in</span> reversed(range(n // <span class="number">2</span>)):</span><br><span class="line">        adjust_heap(nums, i, n)</span><br><span class="line">    <span class="comment"># 调整堆</span></span><br><span class="line">    <span class="keyword">for</span> i <span class="keyword">in</span> range(n - <span class="number">1</span>, <span class="number">-1</span>, <span class="number">-1</span>):</span><br><span class="line">        nums[<span class="number">0</span>], nums[i] = nums[i], nums[<span class="number">0</span>]</span><br><span class="line">        adjust_heap(nums, <span class="number">0</span>, i)</span><br><span class="line">    <span class="keyword">return</span> nums</span><br><span class="line"></span><br></pre></td></tr></table></figure>


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